4.818   y′(x)2 − (4y(x)+ 1)y′(x) +y(x)(4y(x )+ 1) = 0

ODE

y′(x)2 − (4y(x)+ 1)y′(x)+ y(x)(4y(x)+ 1) = 0

ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Independent variable missing, Solve for y′

Mathematica
cpu = 0.0499261 (sec), leaf count = 55

{{                        }  {                        } }
   y(x) → 1ex−4c1 (ex − 2e2c1) , y(x) → 1e2c1+x (e2c1+x − 2)
          4                          4

Maple
cpu = 0.048 (sec), leaf count = 49

{    ln (y (x))         (∘ --------)              ln(y(x))        ( ∘---------)                  1}
 x − --------− Artanh   1 + 4y(x) − -C1 = 0,x − --------+ Artanh   1 + 4y(x) − -C1 = 0,y(x) = −-
        2                                         2                                           4

Mathematica raw input

DSolve[y[x]*(1 + 4*y[x]) - (1 + 4*y[x])*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> (E^(x - 4*C[1])*(E^x - 2*E^(2*C[1])))/4}, {y[x] -> (E^(x + 2*C[1])*(-2
 + E^(x + 2*C[1])))/4}}

Maple raw input

dsolve(diff(y(x),x)^2-(1+4*y(x))*diff(y(x),x)+(1+4*y(x))*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = -1/4, x-1/2*ln(y(x))+arctanh((1+4*y(x))^(1/2))-_C1 = 0, x-1/2*ln(y(x))-ar
ctanh((1+4*y(x))^(1/2))-_C1 = 0